Question: Simplify the following expression: $r = \dfrac{-5t - 20}{-20t - 5}$ You can assume $t \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-5t - 20 = - (5 \cdot t) - (2\cdot2\cdot5)$ The denominator can be factored: $-20t - 5 = - (2\cdot2\cdot5 \cdot t) - (5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $r = \dfrac{(5)(-t - 4)}{(5)(-4t - 1)}$ Dividing both the numerator and denominator by $5$ gives: $r = \dfrac{-t - 4}{-4t - 1}$